等式约束病态总体最小二乘模型的正则化解及其精度评定

利用平差参数间合理的先验信息能够显著提高解的精度。在病态总体最小二乘模型的基础上，引入等式约束条件，建立等式约束病态总体最小二乘模型，构建该模型的约束正则化准则，并根据拉格朗日极值法导出参数的迭代解及方差-协方差阵，最后以数值算例和病态测边网算例验证公式的正确性。结果表明，新方法通过正则化准则能改善法矩阵的病态性，且遵从EIV准则顾及系数阵的误差，同时还考虑参数间合理的先验信息，其解的精度得到显著提升。

A Regularized Solution and Accuracy Evaluation of Ill-PosedTotal Least Squares Problem with Equality Constraints

The accuracy of solutions for ill-posed equations can be significantly improved by using the reasonable equality constraint between the adjustment parameters. In this paper, an ill-posed total least squares model with equality constraints is proposed by applying equality constraints to an ill-conditioned total least squares model. The regularization criterion for constrained ill-posed total least squares is established, and the iterative solution of parameters and its variance-covariance matrix are obtained according to the Lagrangian multiplier method. Finally, numerical examples and ill-posed trilateration network example are used to verify the correctness of the formula. The results show that new method not only improves the ill-posedness of normal matrix by regularization criteria, but also complies with error of coefficient matrix according to EIV criteria. At the same time, it also considers reasonable prior information between parameters; therefore, the accuracy of solution is significantly improved.